Protesters smeared oil-like liquid on the entries in a wildlife photography competition in the central hall of the west London museum.
Camp for Climate Action said their aim was to highlight Shell's "attempts to greenwash its reputation".
The museum said it was pleased to work with Shell saying the firm was taking environmental protection seriously.
The exhibition was closed for cleaning after Saturday's afternoon attack but was expected to re-open on Sunday.
Camp for Climate Action is calling on the museum to end its sponsorship arrangements with Shell.
"This is not an attack on the work of the photographers," said activist Dan Baker.
"Shell does not deserve to have its name associated with their beautiful images."
Companies with operations that threaten the planet look to wildlife as a way of maintaining their image.
Shell and the rest are wrecking our planet's climate. Direct action campaigners will I guess be stepping up their activities against them.
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